Three Dimensional Geometry
Find the vector equation of a line passing through the point and perpendicular to the plane .
Also, find the point of intersection of this line and the plane.
Clearly, the required line passes through the point and is parallel to the normal of the given plane, which is .
So, the required vector equation is
The Cartesian equation of the line is .
A general point on this line is .
For same particular value of let the line cut the plane .
required point of intersection of the line and plane is
, i.e., .